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Number Theory/Coordinate Geometry.


Coordinate Geometry.
Coordinate Geometry.  
Dear Prof Vijilant

What could be the Impact to different disciplines and applications
of mathematics if Point (x,y) is replaced with Point (y,x).

i.e. x coordinate = Horizontal axis
    y coordinate = Vertical axis

Now instead of this standard convention, implement the following
given below

i.e. x coordinate = Vertical axis
    y coordinate = Horizontal axis

For examples :  

1st Quadrant Point A(3,2) will become Point A(2,3)
2nd Quadrant Point B(-2,3) will become Point B(3,-2)
3rd Quadrant Point C(-3,-4) will become Point C(-4,-3)
4th Quadrant Point D(2,-3) will become Point D(-3,2)

i.e. because the Points are now represented as y,x instead of x,y,
the Plotting of Points A,B,C,D on graph paper will be now different.

Can there be any impact while plotting Graphs viz Sine,Cosine, Tangent waves etc, vector algebra and other applications of mathematics similar to Coordinate Geometry if Point F (x,y) is represented as Point F(y,x) ?

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

Hello again
In a busy week with many meetings, I haven't time to look up your references.

All it needs is reflection of a graph in the line y = x.  This will not have any affect on definitions of functions, or on identities or theorems.  As long as all occurrences of x and y as algebraic symbols, (which is normally standard as in Word Equations), are in a different font from textual x,y, it would be easy to write a program to change an electronic version of a book from one form to another.  That sounds like a good ICT project.



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